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Efficient trinomial trees for local‐volatility models in pricing double‐barrier options

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  • U Hou Lok
  • Yuh‐Dauh Lyuu

Abstract

A local‐volatility (LV) model captures the volatility smile while retaining the preference freedom of the Black–Scholes model. Past attempts to construct a smile‐consistent tree for the LV surface do not guarantee validity. This paper presents an efficient and valid smile‐consistent tree for the LV model. The only assumption is that the LV surface be upper‐ and lower‐bounded. With this tree, double‐barrier options can be priced with fast convergence even in the presence of volatility smile. This is confirmed numerically. An implied tree is also presented. It recovers the LV surface reasonably well.

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  • U Hou Lok & Yuh‐Dauh Lyuu, 2020. "Efficient trinomial trees for local‐volatility models in pricing double‐barrier options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(4), pages 556-574, April.
    • Handle: RePEc:wly:jfutmk:v:40:y:2020:i:4:p:556-574
    DOI: 10.1002/fut.22080
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    1. U Hou Lok & Yuh-Dauh Lyuu, 2022. "A Valid and Efficient Trinomial Tree for General Local-Volatility Models," Computational Economics, Springer;Society for Computational Economics, vol. 60(3), pages 817-832, October.
    2. Lu, Yu-Ming & Lyuu, Yuh-Dauh, 2023. "Very fast algorithms for implied barriers and moving-barrier options pricing," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 251-271.

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